False vacuum inflation with Einstein gravity

We present a detailed investigation of chaotic inflation models which feature two scalar fields such that one field (the inflaton) rolls while the other is trapped in a false vacuum state. The false vacuum becomes unstable when the magnitude of the inflaton field falls below some critical value, and a first or second order transition to the true vacuum ensues. Particular attention is paid to the case termed ‘‘hybrid inflation’’ by Linde, where the false vacuum energy density dominates so that the phase transition signals the end of inflation. We focus mostly on the case of a second order transition, but treat also the first order case and discuss bubble production in that context for the first time. False-vacuum-dominated inflation is dramatically different from the usual true vacuum case, both in its cosmology and in its relation to particle physics. The spectral index of the adiabatic density perturbation originating during inflation can be indistinguishable from 1, or it can be up to ten percent or so higher. The energy scale at the end of inflation can be many orders of magnitude less than the value ${10}^{16}$ GeV, which is ususal in the true vacuum case. Reheating occurs promptly at the end of inflation. Cosmic strings or other topological defects are almost inevitably produced at the end of inflation, and if the inflationary energy scale is near its upper limit they contribute significantly to large scale structure formation and the cosmic microwave background anisotropy.

Turning to particle physics, false vacuum inflaton occurs with the inflaton field far below the Planck scale and is therefore somewhat easier to implement in the context of supergravity than true vacuum chaotic inflation. The smallness of the inflaton mass compared with the inflationary Hubble parameter still presents a difficulty for generic supergravity theories. Remarkably, however, the difficulty can be avoided in a natural way for a class of supergravity models that follow from orbifold compactification of superstrings. This opens up the prospect of a truly realistic superstring-derived theory of inflation. One possibility, which we show to be viable at least in the context of global supersymmetry, is that the Peccei-Quinn symmetry is responsible for the false vacuum.